Re: Counterintuitive
You make some excellent points, including spotting that the picture in wide use is a snapshot of a Britain First channel on YouTube, hardly matching the "Islamic extremist" description many others are using (but certainly extremist in their own way).
"is this really about the Guardian being annoyed that it helped fund the BNP?"
The particular names aren't really significant - the "ads in inappropriate places" topic now goes much further than just the New Guardian, which has very little other than the name and Polly Toynbee in common with its illustrious ancestor. Even Will Hutton has recently resigned from the Board of the Scott Trust Limited (which has been and is the Guardian's parent organisation):
https://beta.companieshouse.gov.uk/company/06706464/officers
There was a time in happier days, thirty years ago. when the (older, more principled, less Buzzfeed-like) Guardian ran a series of video/TV adverts based on the principle that things aren't necessarily what they seem at first glance:
https://www.youtube.com/watch?v=_SsccRkLLzU (adblock recommended, as always with YouTube)
Times change.